Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
All structured programs have small tree width and good register allocation
Information and Computation
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
Algorithms and theory of computation handbook
Parity games on graphs with medium tree-width
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Parity games on undirected graphs
Information Processing Letters
Faster algorithms for markov decision processes with low treewidth
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Parity games are a much researched class of games in NP ∩ CoNP that are not known to be in P. Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small. In this paper, we show that, if a tree decomposition is provided, then parity games with bounded treewidth can be solved in O(k3k+2 ·n2 ·(d+1)3k) time, where n, k, and d are the size, treewidth, and number of priorities in the parity game. This significantly improves over previously best algorithm, given by Obdržálek, which runs in $O(n \cdot d^{2(k+1)^2})$ time. Our techniques can also be adapted to show that the problem lies in the complexity class NC2, which is the class of problems that can be efficiently parallelized. This is in stark contrast to the general parity game problem, which is known to be P-hard, and thus unlikely to be contained in NC.